Ultracompact and silicon-on-insulator-compatible polarization splitter based on asymmetric plasmonic dielectric coupling

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1 Appl. Phys. B DOI /s Ultracompact and silicon-on-insulator-compatible polarization splitter based on asymmetric plasmonic dielectric coupling Linfei Gao Feifei Hu Xingjun Wang Liangxiao Tang Zhiping Zhou Received: 30 September 2012 / Accepted: 15 April 2013 Ó Springer-Verlag Berlin Heidelberg 2013 Abstract An ultracompact and silicon-on-insulatorcompatible polarization splitter (PS) is proposed by utilizing asymmetric directional coupling between a hybrid plasmonic waveguide and a strip dielectric waveguide. Owing to the plasmon-assisted asymmetry, birefringence is highly enhanced. Polarization splitting can be realized by strong coupling of one polarization while the other polarization is phase-mismatched. As an example, a PS based on strong TM coupling is demonstrated at the wavelength of 1.55 lm with a coupling length of 4.13 lm. Extinction ratios are 20.9 and 16.4 db for TM and TE polarizations, respectively. The device is also broadband and fabricationtolerant. 1 Introduction Plasmonics is renowned for its excellent ability to break the diffraction limit and thus drive photonic integrated circuits (PICs) to the subwavelength range [1, 2]. However, losses induced by metal hinder applications of plasmonic devices. One emerging and promising approach is to integrate plasmonics with traditional dielectric-based photonics [3 5], for example, with the silicon-on-insulator (SOI) platform which is CMOS-compatible and promising to realize optoelectronic integration. In this way, low-loss SOI waveguides can play the role of bridges between devices for signals long distance propagation, while plasmonic devices can be used locally for specific functions. L. Gao F. Hu X. Wang L. Tang Z. Zhou (&) State Key Laboratory of Advanced Optical Communication Systems and Networks, School of Electronics Engineering and Computer Science, Peking University, Beijing , China zjzhou@pku.edu.cn As the basic elements, various plasmonic waveguides have been developed [2]. Among them, hybrid plasmonic waveguides (HPW) are emerging due to their unique advantages of both long propagation length and strong confinement [6 11]. Moreover, HPWs are compatible with common Si nanowire waveguides on the SOI platform in both fabrication process and propagation modes. The coupling between HPWs and Si waveguides is quite simple and efficient as well [5]. Consequently, HPWs and HPWbased devices pave one of the most promising ways to realize the aforementioned hybrid PICs. Basic properties of HPWs have been investigated [6 11]. However, it is still in great demand to develop HPW-based devices with various functions, such as polarization splitters (PSs), for which plasmonics has unique potential due to its natural polarization sensitivity [1]. PSs are crucial devices for PICs, especially for the SOI platform with high index contrast [12]. Traditionally, PSs are realized by dielectric-based structures [13 17], but there are relatively few designs that can meet the increasingly stringent requirements for devices compactness and ease of fabrication. Most recently, some frontier researches on plasmon-assisted PSs arise. Liu et al. [18] presented a long range surface plasmon polariton (LRSPP)-based PS, but the device size is large (several lm in width and hundreds of lm in length). In Ref. [19] and [20], plasmonic structures with vertical metal ribbons were used to enhance structural birefringence. However, these structures are difficult to fabricate using standard layer-by-layer (bottom to top) processes since they contain horizontal heterostructures at nano scale. In this paper, we propose a novel HPW-based PS, which utilizes asymmetric directional coupling (DC) between an HPW and a strip Si dielectric waveguide (DW). The device is based on an SOI wafer and can be feasibly fabricated in

2 L. Gao et al. similar processes with HPWs [9]. In principle, different from traditional symmetric DC-based PSs consisting of two same waveguides [14], the proposed device utilizes two different types of waveguides to enhance the birefringence, which allows ultrashort splitting lengths and high extinction ratios. Furthermore, it also provides the function to excite hybrid plasmonic mode with the conventional dielectric mode. Therefore, this device itself has well reflected the concept of hybrid PICs. 2 Structure and principle The schematic of the proposed PS is shown in Fig. 1. It consists of an HPW and a strip DW on an SOI wafer with a 340-nm-thick Si top layer. The thin low-index layer in the HPW is SiO 2 with a height of h. The metal cap is Ag with a height of h m = 100 nm. Light is the input from the DW and propagates to the coupling region, in which the two waveguides are adjacent with a proper distance of d, to realize polarization-dependent coupling. Then, the two waveguides carrying different polarizations are separated by an S bending of DW. At the output port of HPW, we can simply use a taper coupler to transmit signals to a DW [5, 9], for experimental characterization or integration with other components conveniently. In addition, the HPW is also able to work as a connection with other HPW-based devices, which is not possible in traditional PSs. The key part of the device is the coupling region. Owing to the asymmetry, the two waveguides could be designed to satisfy the phase-matching condition of only one polarization. Accordingly, the strongly coupled polarization will be transferred from DW to HPW with a proper length of the coupling region (L). By contrast, the weakly coupled polarization will propagate through the DW due to the phase mismatching. Therefore, it is very easy to realize polarization splitting only in a short L, which just needs to be the coupling length of the strongly coupled polarization. Furthermore, compared with traditional symmetric structures where both polarizations could experience strong coupling, the selective coupling of two polarizations is beneficial to obtain high extinction ratios. A single DW can support guided TM mode and TE mode simultaneously with proper dimensions. For a single HPW, most researches have focused on its hybrid plasmonic mode in TM polarization. Actually, it can also support traditional photonic TE mode with proper dimensions [4]. Eigenmodes of a single DW and a single HPW were calculated separately by the finite element method. The operation wavelength is 1.55 lm, and corresponding refractive indices for Ag, SiO 2, and Si are ? i [21], 1.445, and 3.455, respectively. Figure 2 shows the real part of refractive indices for TM and TE modes in HPW and DW (n 1 for HPW and n 2 for DW) as a function of waveguide widths. One sees that n of a certain polarized mode in the two waveguides is different due to the influence of the two additional layers on Si core in the HPW. The impact on TM modes is stronger. Therefore, it is easy to get TM modes phase-matched by choosing appropriate w 1 and w 2, while TE modes are phase-mismatched. For example, if we set h = 50 nm and w 1 = 300 nm, an optimal value of w 2 is 416 nm. The detailed results are shown in Table 1. Moreover, according to Fig. 2, as h decreases, the difference between n 1_TM and n 2_TM is much larger. Consequently, in order to make TM phase-matched at a smaller h, the difference between w 1 and w 2 needs to be larger. This is Table 1 Strong TM coupling condition HPW DW Condition w 1 = 300 nm w 2 = 416 nm TM n HPW_TM = n DW_TM = Strong coupled TE n HPW_TE = n DW_TE = Weak coupled Fig. 1 Schematic of the proposed polarization splitter and the crosssection of the coupling region Fig. 2 The real part of the effective indices of HPW and DW modes versus waveguide width

3 Asymmetric plasmonic dielectric coupling Fig. 3 Normalized electric field distributions of supermodes at strong TM coupling condition. Here, w 1 = 300 nm, w 2 = 416 nm, h = 50 nm, and d = 100 nm beneficial to further differentiate the corresponding n 1_TE and n 2_TE, and thus reduces the cross-talk. Meanwhile, the propagation length of HPW modes decreases as h goes down [7, 8]. Therefore, a proper h should be selected according to various application demands. In the following study, h is set to be 50 nm as an example. When HPW and DW are adjacent enough, they form a superstructure that supports four supermodes, two quasi- TM modes (even and odd), and two quasi-te modes (even and odd). Normalized electric field distributions of the supermodes are shown in Fig. 3. The two supermodes of one certain polarization have different propagation constants; thus, the power exchange between the two waveguides can be represented as their beating. It is also possible to give an analytical solution by the coupled-mode theory [22]. In the case of conventional DCs with symmetric coupling, phase-matched conditions for both polarizations are well satisfied naturally. All the power from the input waveguide can be transferred to the coupled waveguide theoretically. However, in our case of asymmetric coupling, the maximum fraction of exchanged power is related to the phase-matching degree [23]. Specifically, the power exchanged from DW to HPW is j/ðxþj 2 ¼ F sin 2 ðn even n odd Þk 0 x 2 ; ð1þ where F is the maximum fraction of exchanged power, n even and n odd are effective indices of even and odd supermodes for a certain polarization, and k 0 is the propagation constant in free space. When x equals the coupling length L c = p/k 0 (n even - n odd ), the power exchanged to the coupled waveguide reaches a peak value of F. Therefore, the desired condition for polarization splitting is F TM * 1 while F TE * 0. Here, F = 1/(1? d 2 /j 2 ). d is Fig. 4 Real part of the effective indices of even TM mode and odd TM mode versus d. Inset, the coupling length of TM mode versus d the difference between propagation constants of individual guided modes, and d = (n 1- n 2 ) k 0 /2. j is the coupling constant which is related to the fields overlap in the superstructure. In the strong coupling region defined as d/j 1, j could be expressed as a function of the propagation constant of each supermode, j = (n even - n odd ) k 0 /2. n 1 and n 2 mainly depend on dimensions of the single waveguide as we have analyzed above. Here, another important degree of freedom to design the device is the distance d between the two waveguides. d has a direct bearing on n even and n odd. According to Fig. 4, the difference between n even and n odd goes up as d decreases, which leads to a higher F value. Meanwhile, L c can be very short by reducing d as shown in the inset of Fig. 4. For instance, when d = 50 nm, L c_tm is as small as 2.59 lm. Even at a larger d such as 100 nm, which can be easily realized by modern technology, L c_tm is still very small (4.13 lm). Therefore, the configuration paves a practical way to realize ultracompact PSs. 3 Results and discussion In order to verify and characterize the device, 3D simulation by the finite difference time domain method is carried out. The strong TM coupling case (w 1 = 300 nm, w 2 = 416 nm) is taken as an example. In the consideration of application feasibility, d is set to be a moderate value of 100 nm. Figure 5 presents the field distribution for TM and TE polarizations in the coupling region. When TM-polarized light is input in DW, the energy is coupled to HPW and reaches a peak in HPW at L = 4.13 lm, which fits well with the analytical result of L c_tm shown in the inset of Fig. 4. By contrast, when TE-polarized light is input in

4 L. Gao et al. Fig. 5 Electric field distribution of the coupling region with TM or TE polarization input from the left port of DW propagation lengths (214 lm for TM mode and 246 lm for TE mode), while the length of HPW is only 4.13 lm. Therefore, loss induced by metal has little effect here. Fabrication tolerance is also analyzed. Compared with the thickness of each layer, widths of the two waveguides are more difficult to be precisely controlled in fabrication. Figure 6(b) presents transmission as a function of waveguide width variation Dw (w 1 = w 1? Dw, w 2 = w 2? Dw, and d = d-dw). T TE_HPW and T TE_DW are nearly unaffected because TE polarization almost propagates through the DW. By contrast, T TM_HPW and T TM_DW are sensitive to Dw since TM is the coupled component and its phase-matching condition is dependent on w and d. Nevertheless, high extinction ratios (ER TM [ 15 db and ER TE [ 10 db) can still be obtained for a large range of width deviation (-40 nm \ Dw \ 30 nm). 4 Conclusions Fig. 6 Dependence of transmission on a wavelength and b waveguide width deviation DW, it almost experiences no coupling due to the phase mismatch. Consequently, two polarizations are split. Figure 6(a) shows the transmission (T) spectral responses. One sees that T TE_HPW and T TE_DW are not sensitive to wavelength, while T TM_HPW and T TM_DW are wavelength dependent and reach their extreme values around the designed wavelength of 1.55 lm. One of the most significant parameters for a PS is the extinction ratio (ER), which is defined as the ratio between powers of two polarizations at the same output port. For the above case, ER TM ¼ 10 lgðt TM HPW =T TE HPW Þ; ER TE ¼ 10 lgðt TM DW =T TE DW Þ: ð2þ Consequently, ER TM is around 20 db for a large band of 200 nm centered at 1.55 lm, while ER TE is over 14.7 db for the whole C band. At 1.55 lm, ER TM = 20.9 db and ER TE = 16.4 db. In addition, loss is a basic concern for devices, especially for plasmonic devices which usually suffer high loss induced by metal. In the demonstrated structure, however, modes in HPW have relatively long In conclusion, we have designed and investigated an ultracompact and SOI-compatible PS based on asymmetric directional coupling between an HPW and a DW. The device makes full use of similarities and differences between HPW modes and DW modes. Birefringence is highly enhanced compared with traditional symmetric structures. Thus, ultrashort splitting length (4.13 lm) and high extinction ratios are obtained. Furthermore, the device is broadband and tolerant to fabrication errors. This on-chip PS is flexible to be integrated with other components and will enrich various applications such as optical communication and quantum computation. Acknowledgments This work was partially supported by the Peking University 985 startup fund. References 1. W.L. Barnes, A. Dereux, T.W. Ebbesen, Nature 424, 824 (2003) 2. D.K. Gramotnev, S.I. Bozhevolnyi, Nat. Photonics 4, D. Dai, Y. Shi, S. He, L. Wosinski, L. Thylen, Opt. Express 19, (2011) 4. M.Z. Alam, J.S. Aitchison, M. Mojahedi, Opt. Lett. 37, 55 (2012) 5. Y. Song, J. Wang, Q. Li, M. Yan, M. Qiu, Opt. Express 18, R.F. Oulton, V.J. Sorger, D.A. Genov, D.F.P. Pile, X. Zhang, Nat. Photonics 2, 496 (2008) 7. D. Dai, S. He, Opt. Express 17, (2009) 8. L. Gao, L. Tang, F. Hu, R. Guo, X. Wang, Z. Zhou, Opt. Express 20, (2012) 9. M. Wu, Z. Han, V. Van, Opt. Express 18, Q. Li, Y. Song, G. Zhou, Y. Su, M. Qiu, Opt. Lett. 35, V.J. Sorger, Z. Ye, R. Oulton, Y. Wang, G. Bartal, X. Yin, X. Zhang, Nat. Commun. 2, 331 (2011)

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